# Learning Deep Representation with Energy-Based Self-Expressiveness for Subspace Clustering

arXiv: https://arxiv.org/abs/2110.15037 · HTML: https://mlsanity.com/paper/2110.15037/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 43 references that are in the map.
- First posted on arXiv 28 Oct 2021.

## Builds on (most cited first, 23 of 23)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One](https://mlsanity.com/paper/1912.03263/) (2019)
- [Learning Non-Convergent Non-Persistent Short-Run MCMC Toward Energy-Based Model](https://mlsanity.com/paper/1904.09770/) (2019)
- [Deep Structured Energy Based Models for Anomaly Detection](https://mlsanity.com/paper/1605.07717/) (2016)
- [Learning Latent Space Energy-Based Prior Model](https://mlsanity.com/paper/2006.08205/) (2020)
- [Deep Subspace Clustering Networks](https://mlsanity.com/paper/1709.02508/) (2017)
- [ClusterGAN : Latent Space Clustering in Generative Adversarial Networks](https://mlsanity.com/paper/1809.03627/) (2018)
- [Generalized Energy Based Models](https://mlsanity.com/paper/2003.05033/) (2020)
- [Scalable Sparse Subspace Clustering by Orthogonal Matching Pursuit](https://mlsanity.com/paper/1507.01238/) (2015)
- [Robust and Efficient Subspace Segmentation via Least Squares Regression](https://mlsanity.com/paper/1404.6736/) (2014)
- [Oracle Based Active Set Algorithm for Scalable Elastic Net Subspace Clustering](https://mlsanity.com/paper/1605.02633/) (2016)
- [Subspace Clustering by Block Diagonal Representation](https://mlsanity.com/paper/1805.09243/) (2018)
- [Self-Supervised Convolutional Subspace Clustering Network](https://mlsanity.com/paper/1905.00149/) (2019)
- [Structured Sparse Subspace Clustering: A Joint Affinity Learning and Subspace Clustering Framework](https://mlsanity.com/paper/1610.05211/) (2016)
- [Learning a Self-Expressive Network for Subspace Clustering](https://mlsanity.com/paper/2110.04318/) (2021)
- [Stochastic Sparse Subspace Clustering](https://mlsanity.com/paper/2005.01449/) (2020)
- [Correlation Adaptive Subspace Segmentation by Trace Lasso](https://mlsanity.com/paper/1501.04276/) (2015)

## Abstract (arXiv)

Deep subspace clustering has attracted increasing attention in recent years. Almost all the existing works are required to load the whole training data into one batch for learning the self-expressive coefficients in the framework of deep learning. Although these methods achieve promising results, such a learning fashion severely prevents from the usage of deeper neural network architectures (e.g., ResNet), leading to the limited representation abilities of the models. In this paper, we propose a new deep subspace clustering framework, motivated by the energy-based models. In contrast to previous approaches taking the weights of a fully connected layer as the self-expressive coefficients, we propose to learn an energy-based network to obtain the self-expressive coefficients by mini-batch training. By this means, it is no longer necessary to load all data into one batch for learning, and it thus becomes a reality that we can utilize deeper neural network models for subspace clustering. Considering the powerful representation ability of the recently popular self-supervised learning, we attempt to leverage self-supervised representation learning to learn the dictionary. Finally, we propose a joint framework to learn both the self-expressive coefficients and dictionary simultaneously, and train the model in an end-to-end manner. The experiments are performed on three publicly available datasets, and extensive experimental results demonstrate our method can significantly outperform the other related approaches. For instance, on the three datasets, our method can averagely achieve 13.8%, 15.4%, 20.8% improvements in terms of Accuracy, NMI, and ARI over SENet which is proposed very recently and obtains the second best results in the experiments.